A particle of mass m = 3 kg has position vector r(t) = [t2 i + t(1+t)j + 2t2 k] m. Find the velocity and acceleration vector of the particle at t=1.

Here's the solution to your problem.

Given:
Mass $m = 3 \, \text{kg}$
Position vector $\vec{r}(t) = [t^2 \hat{i} + t(1+t)\hat{j} + 2t^2 \hat{k}] \, \text{m}$
This can be written as $\vec{r}(t) = [t^2 \hat{i} + (t+t^2)\hat{j} + 2t^2 \hat{k}] \, \text{m}$.

a) The velocity and acceleration vector of the particle at $t=1$

Step 1: Find the velocity vector $\vec{v}(t)$ by differentiating